Is it true that there is no absolute morality?

[The Grand Nudger]

That's right.  The kind of objective moral truth I'm talking about-- that of a hypothetical best action at all given moments-- is useless in establishing and acting on a moral system.

If objective moral truths are useless in establishing and acting on a moral system then...perhaps, you're not talking about moral truths at all?

Would killing baby Hitler have saved the world, or would it have meant that America never hit the level of ingenuity it has, with advanced sciences that might one day save the world from disease?

That would be a potential moral dilemma of consequentialism, but no dilemma at all for deontological ethics.  Most moral systems contain provisions for competing and limited sup-optimal choices, a concept of choosing the lesser of two evils.  Exceptions for the understandably unforeseen and the unforseeable.  Most moral systems make a distinction between a moral imperative and one's moral competency - our ability to, for whatever reason, adhere to the strictures of our moral opinions.  

What I think would more closely speak to potential objective moralities...is why you leveraged infanticide as the hook of the dilemma, and not just any baby, Hitler.  The "cure all diseases" part is explicit and fits with the metrics- this would be a selectively advantageous outcome.  But killing a kid...and why hitler?  Those two probably have moral opinions behind them...it would be those statements, themselves...that were the moral opinions in question.

Do those moral opinions, that make it wrong to do what hitler did or wrong to kill babies (or whatever it is about them that warranted their inclusion as the engine of dilemma), correlate to moral facts?  

I also have to admit that there's an undertone of theistic absolutism under the hood.  Genetic fitness of a species gives way to other philosophical issues if the species succeeds enough to colonize space, to evolve in new environments, and so on.  Without fast-forwarding and seeing whether a super-species finds out a way to save the Universe from a cold death or whatever, it's hard to know what time scale "best" would involve.

I don't know why the timescale is important at all?  Can't an action be the "best" for that moment?  Do we have to save the universe to present a clearcut example of "best action".  I'd aim lower, our day to day lives, our common interactions.